I'm in the middle of a game, and Chesscube goes into one of its connect-disconnect-connect-disconnect cycles, or kicks me off and won't let me log back in, and when I can log back in, the game has finished and I've lost.

Just happened again. I was in a winning position, and the cycle started again, kicking me off, and eventually dropping the connection. By the time I did get logged back in, the game had finished.